We present the results of a blind search for intervening HI 21cm absorption towards 260 radio sources in the redshift range 0<z<2.74 with the Green Bank Telescope. The survey has the sensitivity to detect sub-damped Ly {alpha} (DLA) systems for HI spin temperatures T_s_/f=100K, and despite the successful re-detection of 10 known 21cm absorbers in the sample, we detect no new absorption lines in the full survey. Sources detected in 21cm absorption were also searched for hydroxyl (OH) 18cm absorption and we re-detect 1667MHz OH absorption towards PKS 1830-211. We searched for intervening HI 21cm absorption along the line of sight in each source achieving a total redshift coverage of {Delta}z=88.64 (comoving absorption path of {Delta}X=159.5) after removing regions affected by radio frequency interference. We compute a 95 per cent confidence upper limit on the column density frequency distribution f(N_HI_) and set a statistical constraint on the spin temperature T_s_ in the range 100-1000K, consistent with prior redshifted optical DLA surveys and HI 21cm emission observations at the same redshifts. We infer a value for the cosmological mass density of neutral gas, {Omega}_HI_. Through comparison with prior {Omega}_HI_ measurements, we place a statistical constraint on the mean spin temperature of T_s_/f=175K. Our derived {Omega}_HI_ values support a relative mild evolution in {Omega}_HI_ over the last 11Gyr and are consistent with other methods that measure {Omega}_HI_.